2
The Big Picture m In the Beer Game, as in real life, there is lots of variability in demand and supply. m Compensating for this through capacity alone is very expensive. m Inventory provides a cheaper alternative, but we need to understand how to use it efficiently.

5
How can inventory help us? Recall the Iron Law of Inefficiency Complexity * Variability = Inefficiency Variability - Supply of raw materials and demand for finished goods often vary with time, making the capacity trade-off very difficult to manage. Inventory Raw Material Inventory allows us to smooth the supply of Raw Materials to Capacity, allowing a smaller capacity to achieve the same throughput. Finished Goods Inventory allows us to use a smoother throughput to satisfy varying demand, again allowing us to use a smaller capacity.

6
How can inventory help us? Consider the following diagram Inventory allows us to store up capacity for use at a later time. This allows us to reduce our capacity from peak down towards average demand. but only at a price! AVG DEMAND PEAK DEMAND DEMAND TIME UNITS/MONTH

10
To summarize, the 3 cases are: 1) No blockage or starvation In = S; Out = D; I = (S-D)*(T end -T beg ) I Tend = I Tbeg + I; I avg = (I Tbeg + I Tend )/2 2) Starvation, i.e. No inventory and S<D In = S; Out = In; I = 0; I Tend = I Tbeg =0 3) Blockage i.e Max inventory and S>D (Sometimes there is no max) In = Out; Out = D; I = 0; I Tend = I Tbeg =I max Trick is to figure out when you switch from one case to another. Inventory Calculations 4 T beg TIME INVENTORY T end I svg

12
Fishing Fleet Calculations A What 3 time periods do we have to worry about? Can be blocked or starved? Find inventory at times 0.0 : : 12.0 : Note to simplify things we use continuous time (0.1, 1.321, 3.0 months) as opposed to discrete time in our calculations (0, 1, 2, 3...).